What is the largest number this tool can handle?

The tool accepts positive integers up to 10^15 (1,000,000,000,000,000). Larger values are rejected with a friendly error. The algorithm uses JavaScript BigInt for exact arithmetic, so there is no floating-point rounding.

How does the primality test work?

The tool uses trial division: it checks divisibility by 2, then by every odd integer from 3 up to the square root of n. For n up to 10^15 the square root is at most ~31,622,776, which is computed in well under a second in a modern browser.

What is prime factorization?

Prime factorization expresses a composite number as a product of prime numbers. For example, 360 = 2^3 × 3^2 × 5. Every positive integer greater than 1 has a unique prime factorization, a fact known as the Fundamental Theorem of Arithmetic.

How are the next and previous primes found?

The tool increments (or decrements) the input by 1 and repeatedly tests each candidate until a prime is found. For typical inputs this takes only a few iterations; in the worst case (a prime gap) it may take a few hundred, still well within milliseconds.

Is the number 1 considered prime?

No. By modern mathematical convention, 1 is neither prime nor composite. The tool reports this explicitly. The smallest prime number is 2.

Prime Number Checker

Name: Prime Number Checker
Availability: InStock
Author: Nham Vu

Enter a number to instantly check if it is prime, see its prime factorization, and find the next/previous primes.

Enter a Number

Positive integer (up to 10¹⁵)

Try an example

Enter a number on the left and click Check

Supports integers up to 1,000,000,000,000,000

Copied!

Summary

Enter a number to instantly check if it is prime, see its prime factorization, and find the next/previous primes.

How it works

Type a positive integer (up to 1,000,000,000,000,000) into the input field.
Click "Check" or press Enter to run the primality test.
Read the large result banner — it clearly states whether the number is prime or composite.
If composite, scroll down to see the complete prime factorization with exponents.
Use the "Copy" buttons next to the previous prime and next prime to copy those values.

Use cases

Verify whether a large number is prime for cryptography or math homework.
Find the prime factorization of a number for least-common-multiple problems.
Locate the nearest prime to any given value when generating RSA key candidates.
Explore the gaps between consecutive primes to study prime distribution.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu